NUCLEAR STRUCTURE AND FORCE
NUCLEAR STRUCTURE AND ''' '''FORCE ' ' ( Revolution in nuclear structure and force by reviving the well-established laws of electromagnetism) By prof. L. kaliambos T.E. Institute of Larissa Greece. Kaliamboslef@Yahoo.gr ''' ' ''This article was announced to many universities around the world (December, 2012 ).'' '''After our published paper “ Nuclear structure is governed by the fundamental laws of electromagnetism” (2003) many physicists try to understand the new ideas about the nuclear structure and force based on natural laws, because after the abandonment of electromagnetic laws due to the assumed uncharged neutron (1932) one can see in “Nuclear structure-WIKIPEDIA” a number of wrong models which cannot lead to the nuclear structure. Also in “Nuclear force-WIKIPEDIA” we see the two contradicting theories of Yukawa (1935) and Gell-Mann (1973) with fallacious force carriers and strange color forces. Note that the paper contains a large number of difficult integral equations and figures which revealed the structure of nuclei. So In order to be undersatndable the new ideas based on laws we present here the Abstract, the Introduction and the Conclusions of the paper ( See in User Kaliambos this published paper alog with the papers "Impact of Maxwell's...dipolic particles" and the "Spin-spin interactions of electrons and also of nucleons create atomic molecular end nuclera structures"). ''Nuclear structure is governed by the fundamental '' laws of electromagnetism ( Published in Ind. J. Th. Phys. Vol. 51 No. 1. 2003) ' '( In order to be understandable it was modified by using only the Abstract, the Introduction and the Conclusions) '' ''L. Kaliambos T. E. Institute of Larissa Greece Abstract Contradicting interpretations of the nuclear force as given by two contrasted approaches like the meson theory and the quantum chromodynamics, are overcome here by reviving the basic electromagnetic laws which are applicable on the existing charged subconstituents in nucleons. On this basis, considerable charge distributions in nucleons as multiples of 2e/3 and -e/3 are determined after a careful analysis of the magnetic moments and the results of the deep inelastic scattering. Basic equations derived from the distributed charges of oriented spins of nucleons give strong and short ranged forces leading exactly to the binding energies of deuteron and other nuclei. According to these interactions, p-p and n-n systems repel and only the p-n bonds form rectangles and closely packed parallelepipeds providing an excellent description of nuclear properties. In this dynamics such contrary forces create structures of saturation and of finite number of nucleons. They also invalidate the charge independence hypothesis and differ widely from the central potential and the effects of the Pauli principle of the electronic configurations responsible for the development of two different models like the Fermi gas and nuclear shell. There are two kinds of p-n bonds, which imply anisotropy, leading often to elongated shapes of vibrational and rotational modes of excitation, while the surface tension contributes to the creation of non elongated shapes with stable arrangements. Finally, for A>40 a type of shell structure provides new rules for understanding the structure of magic nuclei for N>Z and the increasing ratio N/Z with A. Introduction It is indeed unfortunate that the successful discovery of the uncharged neutron 1 along with the enormous strength and very short range of the nuclear force led to the abandonment of the natural electromagnetic laws in favor of qualitative approaches for the study of the nuclear structure, although these laws govern the atomic and molecular interactions. Actually, both the proton and the neutron have fairly large magnetic moments which imply considerable charge distributions, able to create the nuclear structure by giving strong p-n bonds and repelling forces of identical nucleons under quantitative measurements of short ranged dipole-dipole interactions. Nevertheless, after the failure of Heisenberg’s theory 2 and without detailed knowledge about the charged substructure of nucleons, Yukawa’s meson theory 3 seemed to be valid under the discovery of several mesons 4. However, many attempts to fit them into a consistent scheme of nuclear forces did not succeed in reproducing quantitatively the known nuclear phenomena. Another serious problem had to do with the p-p scattering at high energies which is quite different from the p-n scattering, showing that the hypothesis of the charge independence 5 cannot be applied to the scattering data. Moreover, such purely attractive forces of p-n, p-p and n-n systems cannot lead to the saturation 6 and the decay of light nuclei. Thus, in the absence of a realistic force the most important structure models like the liquid drop 7, the Fermi gas 8, the nuclear shell 9, and the collective model 10, lead to complications. H.Ohanian emphasizes that such models are caricatures of the real world 11. On the other hand, the analysis of the deuteron, alone, based on a square- well potential did not give the desired information about the p-n force 12. The same difficulties will be observed, also, in the theory of nuclear matter 13. Of course the aspect of the well-known quantum chromodynamics that the nuclear force is due to the residual strong interaction between the hypothetical color-charged constituents of nucleons 14 cannot provide any framework for quantitative measurements. Moreover, the quark picture 15 could not explain the same phenomena that are treated by the predominant meson theory. Under these conflicting intellectual creations and, starting with the simplest nuclear structure, a satisfactory framework for the quantitative predictions of the simple p-n systems is formulated by reviving the basic electromagnetic laws which are applicable on the existing charge distributions in nucleons of a well described spin in quantum mechanics. In deducing the equations of a realistic inter-nucleon force, detailed knowledge about the interacting charge distributions in nucleons is derived from the g-factors in connection with the results of the deep inelastic scattering. Note that the experimental values of the g-factors of the proton 16 and neutron 17 indicated charge distributions in nucleons confirmed by bombarding them with high-energy electrons 14. Moreover a systematic analysis of the experimental data gives fractional charges as -5e/3 and 8e/3 or 8e/3 and -8e/3 distributed in the centers and along the peripheries of p and n respectively. It is surprising that they have a quark structure since they are proportionally greater than those charges of (uud) and (udd) schemes of the simple quark model. Electromagnetic fields due to such distributed charges favor a coupling of the simple p-n system along the radial direction with S=1 because in this area the motional emf is weaker than that in the direction of the spin axis. Furthermore, quantitative measurements of electromagnetic forces at the shortest separation 2rp for the observed value rp = 0.813 ± 0.008 fm of the proton radius 18 give a p-n bond, whose the binding energy equals the experimental value B(2H)= -2.2246 MeV 5. The simple p-p and n-n systems operate also in radial direction but they give spins of S=0 with repulsive forces. Similarly the electron-electron system operates in radial direction giving S=0 but at a separation r <578.5 fm appears a special attraction able to explain the Pauli principle (bonding state of S=0 in covalent bonds, etc) and the so-called indistinguishability. Under such contrary forces, as in ionic crystals, a close packing of nucleons tends to increase the binding energy B(Z,N) by bringing the unlike nucleons (p-n bonds) closer together with oriented spins which form rectangles and closely packed parallelepipeds, whereas the p-p and n-n systems of repulsion favor a stable structure ,when they are arranged at greater distances (diagonals) with non oriented spins. According to the electromagnetic laws, two deuterons are coupled along the spin axis with S=0 (the motional emf is negligible) involving stronger p-n bonds in axial direction than those in radial one. They form 4He with S=0 which is a two-dimensional rectangle with a coordination number of 2. Despite this small number, 4He is extremely stable since the identical nucleons exert weak repulsions as a result of the non oriented spins and the greater separations (diagonals). Two-dimensional shapes are formed, also, in other light nuclei. However they have B(Z,N)/A smaller than that of 4He due to repulsive forces of additional oriented p-p and n-n systems. On the other hand, the lightest nuclei 3H and 3He have some disorder introduced by a missing nucleon, while in other nuclei, additional neutrons outside closely packed systems make single p-n bonds of weak binding energy often leading to the decay, in contrast to the stable single bond of 2H which has not any p-p or n-n repulsion. Also in 2H there is not any orbital (spatial) motion and in the absence of a motion due to ħ any application of the uncertainty relation or the Schrodinger equation for estimating a repulsive kinetic energy leads to complications. Dramatically, at the beginning of the three-dimensional structure there is a great difficulty for two rectangles to form a simple parallelepiped belonging to the extremely unstable 8Be; this is due to the parallel spin of identical nucleons, repelling with electric and magnetic forces along the diagonals of the squares, so as to reduce significantly the weak radial p-n bonds in a symmetrical shape with a coordination number of 3. Fortunately, for the structure of the heavier α particle nuclei, for A = 12, 16, 20 and 24, proper combinations of rectangles form symmetrical shapes (parallelepipeds) with an increasing coordination number from 3 to 4 or 5 in inner rectangles or squares. This dynamic situation, which implies decrease of the so-called surface tension 7, is able to overcome the repulsions of the oriented p-p and n-n systems to make stable arrangements. Such contrary forces invalidate the charge independence and charge symmetry, as well as the models of the orbital shell and the Fermi gas. Unlike the electronic binding energy per electron, which increases as Z3/4, they lead to the saturation properties and to unstable nuclei. The two kinds of p-n bonds, which imply anisotropy, often lead to elongated shapes of vibrational and rotational modes of excitation described in terms of quanta. High symmetry together with the values of spins 19 and the known binding energies of nuclei 20 are the basic tools for understanding the structure of stable light nuclei, when Z=N, since for a fixed A any change from Z=N to N>Z or N As the nuclei become heavier suitable geometric shapes like tetragonal or orthorhombic systems (cores) are surrounded by outer p-n composite bonds (non single bonds) by increasing the coordination number to the maximum number of 6. This situation implies a significant decrease of the surface tension leading to non elongated shapes with a minimum nuclear surface area. Other polyhedra, as well as spherical or ellipsoidal shapes, are unacceptable because of the oriented spins. Under such a dynamics the outer p-n bonds appear with equal number of p and n and behave like the unfilled shells because they form « empty» positions as many as possible between two or three protons able to receive extra neutrons, which make extra p-n composite bonds in order to overcome the repulsive energies of the dominant long ranged p-p repulsions. In magic nuclei for N>Z, such shells are occupied completely. So, this sort of “shell structure” is responsible for the increasing N/Z with A. The known ratio N/Z along with the symmetry allow us to reveal the structure of magic nuclei and other stable nuclei for odd Z when N>Z. If there are sufficient additional nucleons outside the shape of a magic nucleus, the anisotropy leads to an elongation along the spin axis. In general, a compromise between the surface effect and the anisotropy determines the various shapes of massive nuclei. Such shapes of closely packed nucleons confirm the observable very short distance between nucleons which is comparable to the nuclear size. ' Conclusions' The distributed fractional charges in the spinning nucleons deduced from the o bservable magnetic moments, in connection with the deep inelastic scattering, explain not only the spin S=1 of the simplest structure of 2H, but also give exactly the radial p-n force, since the quantitative measurements, performed in carefully controlled experimentation, lead to the impressive agreement of the calculations with the experimental value B(2H)= - 2.2246 MeV.Such fractional charges which are proportionally greater than the fundamental charges of 2e/3 and -e/3 satisfy the conservation of charge in the beta-decay of n, while the charges of (uud) and (udd) schemes lead to complications. On the other hand , the repulsive energy of the non oriented p-p system in 4He, as calculated by applying the fundamental Coulomb law, is not only in excellent agreement with the p-p repulsion deduced from the observable binding energies of the simplest mirror nuclei, but also it fits into a consistent scheme of binding and repulsive energies in 4He. According to the electromagnetic laws the negligible motional emf in the coupling of two deuterons is responsible for the strong p-n bonds with S=0 along the spin axis. This situation seems to justify the Heisenberg concept of isotopic spin while the simple p-n bonds have always S=1 in radial direction of weak binding energy. Of course the radial energy of -2.2246 MeV and the strong axial energy of -12.4 MeV imply a great anisotropy which explains the rapidly increase of the binding energy from the odd-odd nucleus 2H, to the even-even nucleus 4He, while the asymmetric shape of 3He (odd A) gives an intermediate energy. Also the odd-odd nuclei as 6Li, 10B and 14N are not closely packed in contrast to the α particle nuclei. While the shapes of odd A nuclei as 19F and 23Na are not of high symmetry. These simple examples explain very well the pairing term in the mass formula 32 used for predictions of stability against β decay for numbers of an isobaric family. Such structures show also that the Pauli principle of the electronic configurations is inapplicable in nuclei, since the p-p and n-n systems repel and often are not oriented. For this reason, no bound state is observed for the simple p-p and n-n systems and only in neutron stars the long ranged gravitational energy can hold the repelling neutrons together. Moreover, such repelling forces are responsible for the saturation and the decay of nuclei. In contrast to the shell model here the symmetrical shape of 4He contains non-oriented spins of like nucleons for very stable arrangements, while most of light nuclei contain additional oriented spins of like nucleons reducing the total binding energy. This peculiarity explains the magic number of 2 and the non smooth curve of B(Z,N)/A for light nuclei. From the structure of 4He, it became clear that only the geometry of positions and the orientation of spins of p-n bonds are responsible for holding back the protons. Consequently, the two concepts of charge symmetry and charge independence did much to retard the progress of nuclear physics. Unfortunately the known p-p repulsion seemed to become an attractive force at very short separations, and so far, in vain, nuclear physics aims at the exploration of new natural laws or an unification of different field theories. Accounting for the so-called asymmetry term , a good example is the structure of 6He, in which the imbalance of p and n allows the formation of single p-n bonds of weak binding energy outside the stable rectangle. However, in other light nuclei (and often in massive nuclei) one observes excess neutrons giving stable arrangements, as in the cases of 9Be and 19F, since the additional neutrons make composite p-n bonds connecting two protons for stable arrangements. This fact invalidates the Fermi gas model. On the other hand, according to this model, 8Be should be one of the most stable nuclides. In fact, it splits into two α particles since the identical nucleons with S=1 reduce significantly the radial p-n bonds. That is, as in the decay of massive nuclei the long ranged p-p repulsion along with the short ranged n-n interaction are responsible also for the instability of light nuclei. Note that the application of the uncertainty relation for estimating a huge nuclear force (much more greater than the simple p-p repulsion) leads to complications. In the heavier α particle nuclides for A=12, 16, 20 and 24, the closely packed parallelepipeds explain the peaks of B(Z,N)/A very well since the packing of these shapes increases the coordination number from 3 to 4 or 5. This fact implies a decrease of the surface tension for stable arrangements. The reasons Z=N and S=0 imply high symmetry with a maximum number of p-n bonds, since for a constant A any change from Z=N to N>Z or N In a systematic analysis of the magic numbers 2, 8, 20, 28, 50, 82 and 126 we see that unlike the regular behavior of the electron orbital structure the magic nuclei are only special shapes of very stable arrangements in widely different groups. For example, 4He belongs to the group of a two-dimensional structure, while 16O belongs to the group of parallelepipeds. In the shell structure of the tetragonal system we observe the magic nuclei 40Ca, 48Ca and 64Ni , while the magic nuclei 88Sr and 208Pb belong to another group of orthorhombic systems. As a result the magic nuclei are not related to the noble gases because in the nuclear structure there is not any central potential or any interaction to obey the Pauli principle. Now, it is easy to understand, why in the shell model the use of the hypothetical harmonic oscillator or the spherical-well potential could not reproduce all the data and why the additional postulation of the strong spin-orbit interaction is accompanied with adjustable parameters for reproducing the available data [ 9 ]. According to these postulations, the total potential has the form V= V( r ) - f( r ) L.S where f( r ) is an arbitrary function of the radial coordinates chosen appropriately to fit the available data. Furthermore the shell model cannot explain how in odd-odd nuclei protons and neutrons should couple. Here, a type of shell structure which differs fundamentally from the orbital shells in atoms, favors stable structures after increasing the ratio N/Z with increasing A. This is due to the increasing surface area, able to receive a considerable number of outer p-n bonds for making blank positions as many as possible. More excess neutrons than those of blank positions lead to single bonds (saturated bonds). Therefore, the stability region cannot depart significantly from the line Z=N in the Segre plot 19. The elongation along the spin axis, involving a number of nuclei between the magic nuclei, is explained here by the strong p-n bonds leading to a great anisotropy. However, as the elongation increases very much, a considerable surface tension energy favors the increase of the lattice points with the maximum coordination number of 6 by constructing non elongated shapes withcompleted shells belonging to heavier magic nuclei. Under extreme conditions, this anisotropy leads to super elongated formations exhibiting large quadrupole moments. In general, a dynamic interplay between the surface effect and the anisotropy contributes to the creation of various types of nuclear shapes. This real explanation, based on the electromagnetic interaction of nucleons, is very different from the collective model 10, which presents a great dilemma by using fundamentally different concepts from the nuclear shell and the liquid drop model. Actually, the p-n bonds of oriented spins in the nuclear structure cannot be related to the isotropic material of a liquid drop structure, which gives always spherical shapes neglecting the spins of nucleons. 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